There are many applications for electrical conductors capable of carrying high frequency alternating current (AC). For example, electrical conductors are required to carry high frequency AC between components in high frequency circuits, such as in power conversion circuits or in microwave circuits. As another example, electrical conductors in the form of windings are frequently used to carry high frequency AC in devices which generate an internal magnetic field, such as inductors and transformers, as well as in devices which generate an external magnetic field, such as resonant induction coils. External magnetic fields are used, for example, for induction heating, magnetic hyperthermia, and wireless power transfer.
It can be difficult to transmit high frequency AC through an electrical conductor without incurring significant resistive losses. In particular, a phenomenon known as the “skin effect” causes high frequency AC flowing through a conductor to flow predominately near the conductor's outer surface or “skin,” potentially preventing the electrical conductor's cross-sectional area from being fully used. The skin effect increases with increasing frequency of AC flowing through the conductor, causing effective conductor resistance to increase with increasing frequency. Additionally, current flowing through a conductor will tend to flow along a path which minimizes circuit inductance, which is typically a path which minimizes circuit loop area. This inductive effect, which also increases with increasing frequency, may further constrain AC to a limited portion of a conductor's cross-sectional area. Consequently, a conductor will typically have a significantly higher effective resistance when carrying high frequency AC than when carrying low frequency AC, or when carrying direct current (DC).
FIG. 1 illustrates one example of the skin and inductive effects in a prior art parallel plate transmission line 100 having a first port, a second port, and parallel conductors 102, 104 joining the two ports. Current density through conductors 102 and 104 is approximated by dots on their respective ends 106 and 108. As illustrated, current density is uneven, and the greatest current density occurs near outer portions of conductors 102 and 104 that are facing each other.
One conventional technique for decreasing transmission line resistance is to electrically couple multiple conductors in parallel. At low frequency AC or at DC, effective resistance is approximately inversely proportional to the number of conductors electrically coupled in parallel, assuming that the conductors equally share current. For example, FIG. 2 illustrates a prior art transmission line 200 having a first port and second port. The ports are connected by a first set 202 and a second set 204 of conductor layers. First set 202 includes a number of conductor layers 206 electrically coupled in parallel, and second set 204 includes a number of conductor layers 208 electrically coupled in parallel.
At low frequency AC and at DC, conductor layers 206 of first set 202 have approximately equal effective impedance values and therefore share current substantially equally, and conductor layers 208 of second set 204 have approximately equal effective impedance values and therefore share current substantially equally. At high frequency AC, however, the constituent conductor layers of each set 202, 204 will have different effective impedance values and therefore not equally share current. Instead, current will flow through first set 202 predominately through conductor layers 206 closest to second set 204, and current will flow through second set 204 predominately through conductor layers 208 closest to first set 202. Indeed, if the thickness of conductor layers 206, 208 is small, and if separation between adjacent conductor layers in each set 202, 204 is minimal, transmission line 200 will have a current distribution similar to that of transmission line 100 (FIG. 1) when carrying high frequency AC. Thus, conventional parallel coupling of multiple conductors will typically not achieve low effective resistance when carrying high frequency AC.
High effective resistance may result in significant power loss because conductor power loss is proportional to effective resistance and to the square of current magnitude. Conductor power loss may be undesirable for a number of reasons, such as because conductor power loss impairs conductor power transmission efficiency and causes conductor heating.
As one example of an application which may be sensitive to conductor power loss, consider a system for generating a high-frequency magnetic field. Such a system typically includes an AC power source, such as an inverter, and an induction coil. The AC power source drives AC through the induction coil, thereby causing the coil to generate a time-varying magnetic field. A resonant capacitor is often electrically coupled in series or in parallel with the induction coil to obtain a desired resonant frequency, thereby facilitating driving of the coil. For example, FIG. 3 schematically illustrates a prior art system 300 for generating a high frequency magnetic field. System 300 includes a conventional induction coil 302 forming N winding turns 304 magnetically coupled by a magnetic core 306. Although FIG. 3 shows coil 302 including five winding turns 304 such that N is equal to five, N could be any positive integer greater than zero. A resonant capacitor 308 is electrically coupled in parallel with coil 302, and an AC electric power source 310 drives coil 302 and capacitor 308. Capacitor 308 could alternately be electrically coupled in series with coil 302 and AC electric power source 310.
Voltage (V) across induction coil 302 and capacitor 308 is approximately as follows, where X is a constant for a given coil size and magnetic field strength:V=X·N  EQN. 1
On the other hand, current (I) through winding turns 304 and capacitor 308 is approximately as follows, where Y is a constant for a given coil size and magnetic field strength:I=Y/N  EQN. 2
EQNS. 1 and 2 also hold true in variations of system 300 where capacitor 308 is electrically coupled in series with coil 302, instead of in parallel with the coil.
As can be appreciated from EQNS. 1 and 2, it is not possible to achieve low values of both voltage V and current I in applications where constants X and Y are large. For example, consider magnetic hyperthermia applications, which require a high magnetic field strength. Applicant has conducted simulations to estimate the required root-mean-square (RMS) magnitude of current through a resonant induction coil, and voltage across the coil, to obtain a sufficiently high strength magnetic field in a representative magnetic hyperthermia application. The simulations show that constant X in EQN. 1 must be at least 1,230 volts, and that constant Y in EQN. 2 must be at least 4,380 amperes, to achieve a sufficiently large magnetic field. While the actual values of constants X and Y may vary among magnetic hyperthermia applications, it is anticipated that they will generally have the same order of magnitude as determined in the simulations. Thus, the required current magnitude is very large for a small number of winding turns, and the required voltage magnitude is very large for a large number of winding turns, as shown by EQNS. 1 and 2, assuming constants X and Y are 1,230 volts and 4,380 amperes, respectively.
Large current magnitude results in significant losses in induction coil 302 because it is difficult to achieve low resistance conductors at high frequencies using conventional techniques. For example, increasing cross-sectional area of winding turns 304 will generally not significantly reduce conductor resistance at high frequencies because of skin and inductive effects, as discussed above. Thus, induction coil 302 typically dissipates significant power at high current levels.
High induction coil losses, although undesirable, may be acceptable in some applications. For example, in conventional industrial induction heating systems, winding turns 304 are typically formed of copper tubing, where the tubing serves as both an electrical conductor and a cooling fluid channel. The cooling fluid is circulated through the copper tubing to prevent it from overheating. Although only a portion of the copper tubing conducts current at high frequencies due to skin effects, the tubing's resistance is still typically much lower than resistance of the object (“workpiece”) being heated. Thus, significantly more heat is dissipated in the workpiece than in induction coil 302, potentially resulting in high efficiency, although significant power is lost in the induction coil.
On the other hand, high induction coil losses create significant difficulty in some other applications. For example, high current magnitude is required to achieve a sufficiently high strength magnetic field in magnetic hyperthermia applications when N is small. Such high current magnitude results in more power being dissipated in induction coil 302 than in magnetic nanoparticles used as the “workpiece” in magnetic hyperthermia, so that efficiency is low. In fact, so much power is dissipated in induction coil 302 in typical magnetic hyperthermia applications that the coil must be liquid cooled. A high capacity chiller (not shown), which is typically large, heavy, and expensive, is generally required to remove heat from the cooling liquid. Additionally, AC electric power source 310 must have a high power rating to compensate for coil 302 losses, causing the AC electric power source to also be large, expensive, and heavy. Furthermore, the high power rating of AC electric power source 310 usually requires high capacity electrical service, which is not readily available in most buildings. These factors limit the wide-scale feasibility of magnetic hyperthermia using conventional magnetic field generation technology.
As discussed above, magnitude of current through coil 302 and capacitor 308 can be decreased by increasing N. However, increasing N increases voltage across coil 302 and capacitor 308, which has its own drawbacks. For example, high voltage necessitates high dielectric insulation, which may increase system size, cost, and manufacturing complexity. High voltage also requires use of high voltage rated components, which are often relatively large, costly, and/or difficult to procure. Additionally, high voltage in system 300 may present a safety hazard.
U.S. Pat. No. 6,956,188 to de Rooij et al. proposes an induction heating coil including an integrated resonant capacitor electrically coupled in series or parallel with the resonant coil, thereby potentially eliminating the need for an external resonant capacitor and associated connections. However, de Rooij's coil requires very high voltage magnitude and/or very high current magnitude to generate a high strength magnetic field, in a manner similar to that discussed above with respect to FIG. 3. Additionally, certain embodiments of de Rooij's coil have a helical shape, which may be difficult to manufacture. Furthermore, de Rooij's coil turns may need to be spaced relatively far apart to minimize undesirable inter-turn capacitance, thereby causing the coil to occupy a large volume of space.